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Numerade Educator



Problem 5 Easy Difficulty

Evaluate the integral.
$\int \frac{t}{t^{4}+2} d t$


$\frac{\operatorname{tsin}^{2} t}{2}-\frac{t}{4} \frac{\sin (2 t)}{8}+C$


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Video Transcript

Let's evaluate this one by doing the use of U equals here. The should bad type of there put that A T's winner, not Explorer. Then go ahead and differentiate. So that's our A numerator over here. So after the substitution, we could take out the one half and a girl, do you a top and then we have you squared, plus two. And you made memorize this from the table. But if not, let's go ahead into a tricks up here. All right, so let's plug that in. We get do you of top. So that's rude, too. Sequence Where did better on the bottom You squared to chance flares. What? So we have a toots hands where? Here and then plus two. And instead of writing that to their Limoges right as the one, in fact, there are two Now here we use the fact that tan square plus one sequence where cancel those and we're left with route two of top for in the bottom. And then after cancellation data, let's go ahead and integrate that. That's just data as your constant Siham integration. And then now you can solve for theta using this equation here. So ten equals you over the radical and then take our can on both sides. You over the radical and then plus he and then finally come back up here to your use of to replace you back in terms of tea and I'll be a final answer. You two over four times our ten t squared over the radical plus C, and that's a final answer.